Topic 3  Series and Parallel Circuits

Series Circuits

In a series circuit, the electrons in the current have to pass through all the components, which are arranged in a line.  Consider a typical series circuit in which there are three resistors of value R₁, R₂, and R₃.  The values may be the same, or different.

There are two key points about a series circuit:

• The current throughout the circuit is the same
• The voltages add up to the battery voltage.

Therefore:

V_T = V₁ + V₂ + V₃

From Ohm’s Law we know:

• V_T = IR_T;

• V₁ = IR₁;

• V₂ = IR₂;

• V₃ = IR₃

                                    Þ IR_T = IR₁ + IR₂ + IR₃

Therefore:

Parallel Resistors

Parallel circuits have their components in parallel branches so that an individual electron can go through one of the branches, but not the others.  The current splits into the number of branches there are.  Look at this circuit:

In this case, the current will split into three.   For a parallel circuit we know two things:

• The voltage across each branch is the same
• The currents in each branch add up to the total current.

From this we can write:

I_tot = I₁ + I₂ + I₃

From Ohm’s Law, I = V/R, we can write:

I _T = V ;   I₁ = V;    I₂ = V;   I₃ = V

        R_T          R₁           R₂         R₃

Þ V   =  V +   V  +   V

     R_T     R₁    R₂      R₃

Þ

This is true for any number of parallel resistors

We can combine resistors in both series and parallel.  Tackle the problem step by step.

• Work out the total resistance of the parallel combination.

• Work out the total resistance of the circuit by adding your answer in the previous step to the values of the series resistors.

Here is a worked example:

Take care with such problems:

• Make sure that the voltages across each part of the circuit add up to the battery voltage.

• Make sure the currents in the parallel part of the circuit add up to the battery current.

• If they don’t, go back and check what you’ve done wrong!

We often refer to the total resistance of a circuit as a single resistor equivalent.  Resistors are available in certain values.  One example is the E24 series, in which there are 24 values available in each decade.  For more details, click HERE to go to my electronics notes.  Usually the nearest E24 value will do.  However if a particular value is needed, it can be made from series and parallel combinations of E24 resistors.